NP-Logic Systems and Model-Equivalence Reductions

TL;DR

This paper explores the relationships between different NP-logic systems, showing that existential propositional logic is maximal among NP-systems with NP model checking, but not in the broader NP context.

Contribution

It establishes the maximality of existential propositional logic under poly-time model-equivalence reductions within NP-systems with NP model checking.

Findings

Existential propositional logic ( extit{∃PF}) is maximal among NP-systems with NP model checking.

There exists an NP-system with a D^P-complete model checking problem that challenges maximality.

Model-equivalence reductions help compare the expressive power of NP-logic systems.

Abstract

In this paper we investigate the existence of model-equivalence reduction between NP-logic systems which are logic systems with model existence problem in NP. It is shown that among all NP-systems with model checking problem in NP, the existentially quantified propositional logic (\exists PF) is maximal with respect to poly-time model-equivalent reduction. However, \exists PF seems not a maximal NP-system in general because there exits a NP-system with model checking problem D^P-complete.